Superconductivity and Superfluidity *

Dietrich Einzel

Walther-Meißner-Institut für Tieftemperaturforschung

Bayerische Akademie der Wissenschaften

Outlook:

• Phenomenological description• Superconducting and superfluid systems• Generalized microscopic description

* D. Einzel, Lexikon der Physik, Spektrum Akademischer Verlag, Heidelberg, 2000

Motivation: Physics Nobel prize 2003

Alexei A. Abrikosov (born 1928)Argonne National Laboratory,USA

Vitalii L. Ginzburg (born 1916)P. N. Lebedev Physical InstituteMoscow

Anthony J. Leggett (born 1938) University of Illinois atUrbana-Champaign, USA

Phenomenological description: London vs. Ginzburg-Landau

QM particle with mass M, charge Q, density Ns in external el.mag. Potentials

Quantum-mechanical condensate wave functionF. und H. London, 1935, Max von Laue, 1938, V. L. Ginzburg und L. L. Landau, 1950

Schrödinger equation

charge-supercurrent

Neutral masssupercurrent

Application: pairs

Merits of the London theory

Persistent currentsMagnetic field screeningFluxoid quantisationJosephson effectsGauge invariance

The London theory does not explain:

Q=2e Microscopic origin of Ns

Non-local effectsFlux linesInterfaces

Ginzburg-Landau- and Abrikosov Theory (V. Ginzburg and L. Landau, 1950, A. Abrikosov, 1956)

Merits of the Ginzburg-Landau-and Abrikosov theory

The Ginzburg-Landau- and Abrikosov theory does not explain:

All London resultsNon-local effectsDistinction: type-I and type-IIFlux line lattice Arbitrary boundary conditionsThousands of citations

Q=2e Microscopic origin of Ns

Behavior at lower temperatures T<<Tc

Superconducting and superfluid systems

System Fermi/Bose SC/SF Tc[K] Discovery Nobel prize

Hg Fermi SC 4.2 1911 1913

Liquid 4He BoseSF 2.17 1924 - 1938 1978

A15

compoundsFermi SC 20 1954, 1973 -

Pulsars Fermi SF 108 1968 -

Liquid 3HeFermi SF 10-3 1971 1996

Superconducting and superfluid systems (ctd.)

System Fermi/Bose SC/SF Tc[K] Discovery Nobel prize

Heavy

Fermions Fermi SC 1 1979 -

Organic

SC‘sFermi SC 10 1979 -

Cuprates Fermi SC 100 1986 1987

Sr2RuO4 Fermi SC 1 1993 -

Molecular

HydrogenBose SF 0.2 2000 -

Current relaxation in normal Fermi liquids

Charged Fermions in metals

Neutral Fermi liquids

Drude‘slaw

Hagen-Poiseuille‘s

law momentum conservation(exception: walls)

momentum relaxation:impurities, Phonons...

Indications of superconductivity:Vanishing resistance Heike Kamerlingh-Onnes, 1911

Indications of superfluidity:Vanishing shear viscosity (?)J. M. Parpia, D. Einzel., 1987

viscosity paradox

„GUT“ of superconductivity and superfluidity

charged neutral

Fermi Bose

spin singlet spin triplet even parity odd parity

BCS „non-BCS“

conventionel unconventionel

Aspects andsystems to be unified:

Restrictions:

pair correlated Fermi systems

weak coupling limit

parabolic bands in D=3 und D=2

BCS mean field treatment of superconductivity and superfluidity

Pair attraction nearthe Fermi surface

Spontaneous pair formation in k-space: pair (Gor‘kov-) amplitude

Pair potential (energy gap)

Broken gaugesymmetry

Classification of pair potentials

A. Spin structure

Pauli principle:

Singlet (s=0): even parity

Triplet (s=1): odd parity

Classification of pair potentials (ctd.)

B. Orbital structure

Conventional pairing

shares the symmetry of the Fermi surface;only gauge symmetry broken

Examples: classical singlet SC‘s like Hg, Al, V, ...

Unconventional pairing

has lower symmetry as the Fermi surface;additional broken symmetries

Examples: see next slide

(Moritz, 11 years)

The broken lattice symmetry in cuprates

Conventional and unconventional

model pairing states:

System NameNode-

structure

conv.

SC‘s 1 - isotropic

3He-A

UBe13

Axial (3D)

3He-B -

pseudo-

isotropic

UPt13

- E1g

E2u

Cuprates

(hole-

doped)

-

B1g

Sr2RuO4

Axial (2d)

B1g x Eu

S=0: singletS=1: triplet

The d-wave controversy in the High-Tc community

PHYSICS TODAY MAY 1993

IN HIGH-TC SUPERCONDUCTORS,IS d-WAVE THE NEW WAVE?

BARBARA GOSS-LEVIPHYSICS TODAY

PHYSICS TODAY FEBRUARY 1994

IN EXPLAINING HIGH-TC,IS d-WAVE A WASHOUT?

PHILIP W. ANDERSONPRINCETON UNIVERSITY

BCS mean field treatment of superconductivity and superfluidity (ctd.)

Hamiltonian for spin singlet pairing(triplet pairing:A. J. Leggett, 1965)

Nota bene: the energy

or Nambu space (Yoishiro Nambu, 1962)

is a matrix in particle-hole space

Nota bene: spontaneous pair formation

„off-diagonal long range order“ (ODLRO)

Bogoliubov-Valatin- diagonalisation

Excitation spectrum ofBogoliubov-quasiparticles

Quasiparticle Hamiltonian

Momentum distributionof Bogoliubov-quasiparticles

0

np

(Ep)

/kT

Linear response of the quasiparticle system

External perturbations

Thermal excitationsin local equilibrium

temperature change

magnetic field

vector potential

Thermally activated vs. nodal quasiparticles

Ampere Zeeman

temperature

Linear response of the condensate (BCS-Leggett theory)

Macroscopiclimit

Broken gaugesymmetry

Broken spin-orbit symmetry(SBSOS)Leggett, 1971

Charge supercurrent

New: spin supercurrent

0 1

2

0

1

T/Tc

isotropic

axial

B1g, E1g,

E2u

C(T)/CN(T)Heat capacity ofBogoliubov-quasiparticles

Spin susceptibilityof Bogoliubov-quasiparticles

1

0

0 1T/Tc

axial

pseudoisotropic

B1g, E1g

E2u

isotropic

(T)/N

0

1

0

1T/Tc

isotropic

E1g(||)

E2u

B1g

E1g( )

Bogoliubov quasiparticlecurrent and magneticfield penetration depth

L(T)/L(0)

The unconventional superconductivity in UPt3 (J. A. Sauls et al., 1996)

singlet even parity (E1g) triplet odd parity (E2u)

Selected experimental results

A. Quasiparticle heat capacity

Vanadium and Tin UBe13 (H.-R. Ott et al., 1983)

Selected experimental results (ctd.)

YBa2Cu3O7

(Junod et al., 1996) Sr2RuO4

(Deguchi et al., 2000)

A. Quasiparticle heat capacity

T[K]

C(T)/CN(T)

Selected experimental results (ctd.)

B. Quasiparticle spin susceptibility

GdBa2Cu3O7 (Janossy et al. 1997)

Aluminium

Selected experimental results (ctd.)

B. Quasiparticle spin susceptibility

3He-A, B(Ahonen et al., 1976)

3He-A

3He-B

,

Selected experimental results (ctd.)

C. Magnetic field penetration depth

Mercury UBe13

F. Gross et al., WMI, 1985

Selected experimental results (ctd.)

C. Magnetic field penetration depth

UPt3 (S. Schöttl et al., WMI, 1999)

YBa2Cu3O7

(W. Hardy et al., 1994)

Selected experimental results (ctd.)

D. Electronic Raman scattering

Bi 2212 (Hackl et al., WMI, 1994)

Nb3Sn (Hackl et al., 1989)

Conventional

superconductors

0

1

2

3

E g

Inte

nsi

ty (cp

s/m

W)

Raman shift (cm )w - 1

0 50 100

6 K

19 K

Nb Sn

T = 18 K3

c

Hackl et al., Physica C , 431 (1989)162-164

Cuprate

superconductors

0

2

4

6

8

10Bi- 2212T = 86 Kc

0 200 400 600Raman shift (cm )w - 1

20 K

A1g

B1g

B2gIn

tensi

ty (cp

s/m

W)

Devereaux et al., PRL , 3291 (1994)72

Summary and conclusion: superconductivity and superfluidity

Physics Nobel prize 2003

Overwhelming application spectrum of the work by Vitalii Ginzburg, Alexei Abrikosov und Tony Leggett

Normal state of pair-correlated Fermi systems

Momentum relaxation and Drude conductivityMomentum conservation, shear viscosity and Hagen-Poiseuille law

Generalized BCS model of superconductivity and superfluidity

Parabolic Bands in D=3 und D=2Weak coupling limit Model pairing states

Superfluid 3He

First unconventional BCS superfluid (p-wave triplet pairing)Quantitative results for response und transport propertiesImplications for unconventional metallic superconductors

Unconventional superconductors

Singlet d-wave vs. triplet p- or f-waveNodal quasiparticles and low temperature power lawsApplication to Heavy Fermion SC‘s, organic SC‘s, Cuprates, Sr2RuO4

Future prospects: superconductivity and superfluidity

Unconventional superconductivity, pairing symmetries, mechanisms, transport prop‘s.

Electron-doped cuprates Hole-doped cuprates: full doping dependenceHeavy Fermion SC‘s: UPt3, UBe13, ...Organic superconductorsThe Ruddlesden-Popper system Sr2Ru04

Dirty Fermi superfluids: 3He in aerogel

Local ResponseTransport and RelaxationZero SoundSpin wavesMultiple spin echosPair vibration modes

Two-fluid description of pair-correlated Fermi systems

Transport propertiesThermoelectric/mechanic effectsAnalytic treatment of the quasiparticle response and transport

Appendix A: Matthiessen rule classification

transport in metals transport in cleanFermi liquids

transport in dirtyFermi liquids

(3He in aerogel)

momentum conservation

momentum relaxation(el. + inel.)

momentumrelaxation(elastic)